Question

What are the vertex and x-intercepts of the graph of y=x2-2x-24

Answer 1

Answer:

The vertex of the provided equation (1,-25)

The x intercepts are (-4,0) and (6,0).

Step-by-step explanation:

Consider the provided equation.

$y=x^2-2x-24$

Substitute y=0 to find x intercepts.

$x^2-2x-24=0$

The above equation can be written as:

$x^2+4x-6x-24=0$

$x(x+4)-6(x+4)=0$

$(x+4)(x-6)=0$

By zero product rule:If ab=0 then either a=0 or b=0

$x+4=0$ or $x-6=0$

$x=-4$ or $x=6$

Hence, the x intercepts are (-4,0) and (6,0).

If the equation is in the standard form $y=a^2+bx+c$ then the expression $\frac{-b}{2a}$ gives the x coordinate of the vertex.

By comparing the provided equation with standard form we can concluded that: a=1, b=-2 and c=-24

Substitute the respective values in the expression $\frac{-b}{2a}$ we get x coordinates of the vertex:

$\frac{-(-2)}{2(1)}=\frac{2}{2}=1$

Hence, the value of x=1.

Now substitute the value of x in the provided equation to find the value of y.

$y=(1)^2-2(1)-24$

$y=1-2-24$

$y=-25$

Hence, the vertex of the provided equation (1,-25)

Answer 2

Answer:

Vertex (1,-25), Intercepts at (6,0) and (-4,0)

Step-by-step explanation:

Axis of symmetry = -b/2a = -(-2)/2(1) = 2/2 = 1 so x=1 is the equation of line

Plug x=1 into equation y=1-2-24=-25

factor for x-intercepts:  (x-6)(x+4)

set them equal to zero: x-6=0 so x=6   x+4=0 so x= - 4